The performance of tau-lepton reconstruction and identification algorithms is studied using a data sample of proton-proton collisions at sqrt(s)=7 TeV, corresponding to an integrated luminosity of 36 inverse picobarns collected with the CMS detector at the LHC. The tau leptons that decay into one or three charged hadrons, zero or more short-lived neutral hadrons, and a neutrino are identified using final-state particles reconstructed in the CMS tracker and electromagnetic calorimeter. The reconstruction efficiency of the algorithms is measured using tau leptons produced in Z-boson decays. The tau-lepton misidentification rates for jets and electrons are determined.